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Add problem statements and inputs
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 09 Jan 2018 21:51:44 -0500
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1 --- Day 15: Dueling Generators ---
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2
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3 Here, you encounter a pair of dueling generators. The generators,
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4 called generator A and generator B, are trying to agree on a sequence
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5 of numbers. However, one of them is malfunctioning, and so the
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6 sequences don't always match.
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7
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8 As they do this, a judge waits for each of them to generate its next
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9 value, compares the lowest 16 bits of both values, and keeps track of
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10 the number of times those parts of the values match.
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11
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12 The generators both work on the same principle. To create its next
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13 value, a generator will take the previous value it produced, multiply
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14 it by a factor (generator A uses 16807; generator B uses 48271), and
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15 then keep the remainder of dividing that resulting product by
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16 2147483647. That final remainder is the value it produces next.
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17
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18 To calculate each generator's first value, it instead uses a specific
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19 starting value as its "previous value" (as listed in your puzzle
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20 input).
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21
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22 For example, suppose that for starting values, generator A uses 65,
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23 while generator B uses 8921. Then, the first five pairs of generated
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24 values are:
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25
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26 --Gen. A-- --Gen. B--
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27 1092455 430625591
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28 1181022009 1233683848
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29 245556042 1431495498
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30 1744312007 137874439
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31 1352636452 285222916
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32
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33 In binary, these pairs are (with generator A's value first in each
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34 pair):
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35
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36 00000000000100001010101101100111
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37 00011001101010101101001100110111
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38
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39 01000110011001001111011100111001
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40 01001001100010001000010110001000
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41
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42 00001110101000101110001101001010
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43 01010101010100101110001101001010
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44
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45 01100111111110000001011011000111
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46 00001000001101111100110000000111
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47
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48 01010000100111111001100000100100
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49 00010001000000000010100000000100
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50
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51 Here, you can see that the lowest (here, rightmost) 16 bits of the
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52 third value match: 1110001101001010. Because of this one match, after
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53 processing these five pairs, the judge would have added only 1 to its
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54 total.
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55
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56 To get a significant sample, the judge would like to consider 40
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57 million pairs. (In the example above, the judge would eventually find
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58 a total of 588 pairs that match in their lowest 16 bits.)
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59
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60 After 40 million pairs, what is the judge's final count?
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61
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62 Your puzzle answer was 626.
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63
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64 --- Part Two ---
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65
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66 In the interest of trying to align a little better, the generators get
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67 more picky about the numbers they actually give to the judge.
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68
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69 They still generate values in the same way, but now they only hand a
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70 value to the judge when it meets their criteria:
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71
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72 Generator A looks for values that are multiples of 4.
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73
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74 Generator B looks for values that are multiples of 8.
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75
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76 Each generator functions completely independently: they both go
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77 through values entirely on their own, only occasionally handing an
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78 acceptable value to the judge, and otherwise working through the same
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79 sequence of values as before until they find one.
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80
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81 The judge still waits for each generator to provide it with a value
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82 before comparing them (using the same comparison method as before). It
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83 keeps track of the order it receives values; the first values from
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84 each generator are compared, then the second values from each
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85 generator, then the third values, and so on.
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86
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87 Using the example starting values given above, the generators now
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88 produce the following first five values each:
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89
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90 --Gen. A-- --Gen. B--
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91 1352636452 1233683848
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92 1992081072 862516352
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93 530830436 1159784568
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94 1980017072 1616057672
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95 740335192 412269392
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96
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97 These values have the following corresponding binary values:
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98
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99 01010000100111111001100000100100
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100 01001001100010001000010110001000
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101
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102 01110110101111001011111010110000
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103 00110011011010001111010010000000
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104
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105 00011111101000111101010001100100
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106 01000101001000001110100001111000
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107
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108 01110110000001001010100110110000
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109 01100000010100110001010101001000
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110
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111 00101100001000001001111001011000
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112 00011000100100101011101101010000
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113
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114 Unfortunately, even though this change makes more bits similar on
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115 average, none of these values' lowest 16 bits match. Now, it's not
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116 until the 1056th pair that the judge finds the first match:
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117
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118 --Gen. A-- --Gen. B--
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119 1023762912 896885216
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120
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121 00111101000001010110000111100000
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122 00110101011101010110000111100000
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123
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124 This change makes the generators much slower, and the judge is getting
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125 impatient; it is now only willing to consider 5 million pairs. (Using
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126 the values from the example above, after five million pairs, the judge
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127 would eventually find a total of 309 pairs that match in their lowest
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128 16 bits.)
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129
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130 After 5 million pairs, but using this new generator logic, what is the
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131 judge's final count?
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132
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133 Your puzzle answer was 306.
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134
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135 Both parts of this puzzle are complete! They provide two gold stars: **